Question

3. What is the phase difference between driving force and velocity of the

forced oscillator?​

Answer 1

Governing equation for the Single Degree Freedom System, shown in figure, is

mx¨+kx+cx˙=F0sinωt

Where,

m= mass, k= Stiffness of the spring, c= Damping Coefficient

F0= Amplitude of Excitation, ω= Frequency of Excitation

x= Displacement measured from Static Equilibrium position

x˙= Velocity and x¨= Acceleration

Solution of the governing equation is

x=X0sin(ωt−ϕ)

where, ϕ= phase difference between Force and the displacement.

x˙=ωX0cos(ωt−ϕ)

Or,

x˙=ωX0sin(ωt−ϕ+π/2)

So, the phase difference between Force and the velocity will be ( pi/2−ϕ)

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Answer 2

Answer:

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Governing equation for the Single Degree Freedom System, shown in figure, is

mx¨+kx+cx˙=F0sinωt

Where,

m= mass, k= Stiffness of the spring, c= Damping Coefficient

F0= Amplitude of Excitation, ω= Frequency of Excitation

x= Displacement measured from Static Equilibrium position

x˙= Velocity and x¨= Acceleration

Solution of the governing equation is

x=X0sin(ωt−ϕ)

where, ϕ= phase difference between Force and the displacement.

x˙=ωX0cos(ωt−ϕ)

Or,

x˙=ωX0sin(ωt−ϕ+π/2)

So, the phase difference between Force and the velocity will be ( pi/2−ϕ)

The following figure shows phasors for displacement, velocity, acceleration and the force of excitation.